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Are large distance Heegaard splittings generic?
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October 5, 2011
Abstract
In a previous paper, Journal of Topology 3 (2010), 691–712, we introduced a notion of “genericity” for countable sets of curves in the curve complex of a surface Σ, based on the Lebesgue measure on the space of projective measured laminations in Σ. With this definition we prove that for each fixed g ≧ 2 the set of irreducible genus g Heegaard splittings of high distance is generic, in the set of all irreducible Heegaard splittings. Our definition of “genericity” is different and more intrinsic than the one given via random walks.
The Appendix fixes a small gap in the proof in Kerckhoff, Topology 29 (1990), 27–40, that the limit set of the handlebody set has measure zero.
Received: 2010-02-25
Revised: 2011-03-16
Published Online: 2011-10-05
Published in Print: 2012-09
©[2012] by Walter de Gruyter Berlin Boston
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- Boundary value problems on planar graphs and flat surfaces with integer cone singularities, I: The Dirichlet problem
- Are large distance Heegaard splittings generic?
- The C*-algebra of a vector bundle
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Articles in the same Issue
- Canonical subgroups over Hilbert modular varieties
- Boundary value problems on planar graphs and flat surfaces with integer cone singularities, I: The Dirichlet problem
- Are large distance Heegaard splittings generic?
- The C*-algebra of a vector bundle
- On the modular interpretation of the Nagaraj–Seshadri locus
- Handle addition for doubly-periodic Scherk surfaces
- On the resonances and eigenvalues for a 1D half-crystal with localised impurity
